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To find the **effective rate** given a nominal rate compounded quarterly, you can use the following formula:

\[
\text{Effective Rate} = \left( 1 + \frac{r}{n} \right)^n - 1
\]

Where:
- \( r \) is the nominal rate (expressed as a decimal)
- \( n \) is the number of compounding periods per year

In this problem:
- The nominal rate \( r \) is \( 8\% = 0.08 \)
- The compounding frequency is **quarterly**, so \( n = 4 \)

Let's substitute and solve:

\[
\text{Effective Rate} = \left( 1 + \frac{0.08}{4} \right)^4 - 1
\]

\[
\text{Effective Rate} = \left( 1 + 0.02 \right)^4 - 1
\]

\[
\text{Effective Rate} = (1.02)^4 - 1
\]

Now calculate:

\[
(1.02)^4 = 1.08243216
\]

\[
\text{Effective Rate} = 1.08243216 - 1 = 0.0824
\]

Converting to a percentage and rounding to two decimal places:

\[
\text{Effective Rate} = 8.24\%
\]

**Answer: 8.24% per year**

Would you like further details or have any questions?

Here are some related questions to expand on this topic:

1. What is the difference between nominal and effective interest rates?
2. How does compounding frequency affect the effective interest rate?
3. If the compounding was done monthly, how would the effective rate change?
4. Can you derive the formula for effective rate for a different compounding period, such as semi-annually?
5. How does the effective rate change if the nominal rate increases while keeping the same compounding period?

**Tip:** When working with different compounding frequencies, remember that the more frequent the compounding, the higher the effective interest rate will be compared to the nominal rate.

Find the effective rate corresponding to the given nominal rate of 8% per year compounded quarterly. Use a 365-day year. Round your answer to two decimal places.

Learn how to calculate the effective interest rate from a nominal rate of 8% per year, compounded quarterly. This problem uses the compound interest formula and is suitable for high school students in Grades 9-12.

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